Hi, you're correct, the game only treats the area your screen is in as "active." Inactive places will freeze in time in which collectables will not spawn (plants won't grow, stones won't pop etc.) typically a collectable takes 24 Sim hours to re-spawn, but plants have different lifecycle which I recommend you to check out blogs for detail. However, the game do have mechanics to clean up dishes when you revisit the area, which makes it seems active but actually not.
As for your active lot issue, I've encountered it once and fixed it with game repairing. To do that, right-click TS4 box art and select "repair the game."
Hope this helps.
